Triangulation and navigation

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Greek team workshop animated during the Comenius metting in Rome

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Triangulation and navigation

  1. 1. COMENIUS PROGRAM Measuring the Earth Through European students' Research and collaboration M.E.T.E.R.
  2. 2. COUNTRIES (CITIES) PARTICIPATING IN THE PROGRAM 1. FRANCE (LYON) 2. ENGLAND (BIRMINGHAM) 3. THE NETHERLANDS (AMSTERDAM) 4. ITALY (ROME) 5. ROMANIA (ORADEA) 6. GREECE (ATHENS)
  3. 3. 2nd MEETING IN ROME Topic: Triangulation and Navigation Aim of the Experiment : To measure the distance of two points A and B when there is an obstacle in between Α. Β. How we confront the problem: Starting from point A, we move in a peripheral motion around the obstacle. The way we move is such in order to follow straight lines that are perpendicular between each other.
  4. 4. A B Using the compass below we distinguish the horizontal (green) and the verical movements (red). We also define, with this compass, the movements to the right upward direction as positive while, on the other hand, the movements to the left downward direction as negative.
  5. 5. We measure how many meters we move each time and fill in the results in the following table. RED DIRECTION (+ OR -) GREEN DIRECTION (+ OR -) We add algebraically the measuments separately in the two columns and jot down the results. RED SUM : …............. GREEN SUM : …............. Finally, we apply the Pythagorean theory and calculate the distance between points A and B. (DISTANCE)2 = (RED SUM)2 + (GREEN SUM)2 A B
  6. 6. 3rd MEETING IN ORADEA Topic: Time Who is born giant, reaches manhood * and ages again becoming a giant? It is the shadow of a body Illuminated by the Sun Like the shadow of gnomon of a solar clock whose slow course over the signs of hours and with air of another era gives us a sense from the scent of a different rhythm of life. Aim of the experiment: Measuring time with the help of a solar clock. The construction of a horizontal solar clock: A. DIAGRAM OF HOURS We draw a circle radius R. We cut the circle in half and keep one semi-circle. We place the semi-circle in a horizontal surface and divide the circle in pieces, each corresponding to a 150 angle. We create a system of axes, naming it W(est), E(ast), N(orth), S(outh) - - since the diagram is in Greek, and for your convenience, the equivalence is ∆ (=W), Α (=E), Β (=S), and Ν (=S).
  7. 7. Using point O as the center of the circle as well as the use of a thread we extend the radiuses of the circle and mark their traces on the straight line ∆Α (WE) which osculates on the semi-circle at point K. We extend radius OK and mark ΚΟ΄ whose length is ΚΟ΄=ΚΟ/sinφ where φ the geographical length of the place we want to put the clock. (For Athens the geographical length is approximately 380). From point Ο΄ we τα ευθύγραµµα τµήµατα που ενώνουν το Ο΄ µε τα ίχνη που είχανε προσχεδιάσει. We draw a circle or ellipse or square and the diagram of hours is ready.
  8. 8. A. GNOMON The gnomon, whose shape follows underneath, is a chageable construction. Its dimensions bear a relation to the dimensions of the diagram of hours and have to be such so that side ΑΒ forms angle φ with the horizontal axis and casts shadow cutting the ellipse of the diagram of hours. Β Α φ The direction of the gnomon almost targets the North Pole. Also, the axis of rotation of Earth targets as well the North Pole, in other words, both materialize into almost parallel straight lines.

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